Human hair grows at a rate of about 6.849×10−4 cm per hour to 2.329×10−2 cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation. Do not round your answer.(1 point)
To find the difference between the high end and low end of the range, we subtract the low end from the high end.
High end: 2.329 × 10^(-2) cm per hour
Low end: 6.849 × 10^(-4) cm per hour
Difference = 2.329 × 10^(-2) - 6.849 × 10^(-4)
To subtract the numbers in scientific notation, we need to have the same power of 10. To do so, we can rewrite the low end as 6.849 × 10^(-4) = 0.6849 × 10^(-3) cm per hour.
Difference = (2.329 × 10^(-2)) - (0.6849 × 10^(-3))
Now we can subtract the two numbers:
Difference = 2.329 × 10^(-2) - 0.6849 × 10^(-3)
Difference = 2.329 × 10^(-2) - 0.6849 × 10^(-3) = 2.2601 × 10^(-2) cm per hour.
Therefore, the difference between the high end and low end of the range is 2.2601 × 10^(-2) cm per hour.
To find the difference between the high end and low end of the range, we simply subtract the low end from the high end:
Difference = High end - Low end
Difference = (2.329 × 10^(-2) cm/h) - (6.849 × 10^(-4) cm/h)
To subtract the values in scientific notation, we need to have the same exponent. We can convert 6.849 × 10^(-4) cm/h to the same exponent as 2.329 × 10^(-2) cm/h by multiplying by 10^(2):
Difference = (2.329 × 10^(-2) cm/h) - (6.849 × 10^(-4) cm/h × 10^(2))
Simplifying,
Difference = (2.329 × 10^(-2) cm/h) - (6.849 × 10^(-2) cm/h)
Now that the exponents are the same, we can subtract the mantissas:
Difference = 2.329 × 10^(-2) cm/h - 6.849 × 10^(-4) cm/h
Difference = 2.329 × 10^(-2) - 6.849 × 10^(-4)
Difference = 2.329 × 10^(-2) - 0.006849 × 10^(-2)
Difference = (2.329 - 0.006849) × 10^(-2)
Difference = 2.322151 × 10^(-2) cm/h
Therefore, the difference between the high end and low end of the range is 2.322151 × 10^(-2) cm/h.
To find the difference between the high end and the low end of the range, we need to subtract the low end from the high end.
The low end of the range is 6.849×10^(-4) cm per hour, and the high end of the range is 2.329×10^(-2) cm per hour.
Subtracting the low end from the high end:
2.329×10^(-2) cm per hour - 6.849×10^(-4) cm per hour
When subtracting numbers in scientific notation, it is important to have the same exponent. So, we need to rewrite both numbers with the same exponent.
Since 10^(-4) is smaller than 10^(-2), we can rewrite the low end as:
6.849×10^(-4) cm per hour = 6.849×10^(-4) × (10^(-2) / 10^(-2)) = 6.849×10^(-4) × 10^(-2) cm per hour = 6.849×10^(-6) cm per hour
Now we can subtract the numbers:
2.329×10^(-2) cm per hour - 6.849×10^(-6) cm per hour = 2.329×10^(-2) - 6.849×10^(-6) cm per hour
To subtract these numbers, we keep the same exponent and subtract the coefficients:
2.329 - 6.849×10^(-6) = 2.329 - 0.000006849 = 2.328993151
Now, we express the result in scientific notation. Since the number 2.328993151 has several decimal places, we can write it as:
2.328993151 × 10^0
So, the difference between the high end and the low end of the range is approximately 2.328993151 × 10^0, where the exponent is 0.